Regional

“Math is Cool” Masters – 2012-13
Sponsored by:
November 2, 2012
7th & 8th Grade Mental Math Contest
Follow along as your proctor reads these instructions
to you. Your Mental Math score sheet is on the back.
GENERAL INSTRUCTIONS applying to all tests:
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Good sportsmanship is expected throughout the competition by all involved, both competitors and
observers. Display of poor sportsmanship may result in disqualification.
Calculators or any other aids may not be used on any portion of this contest.
Unless stated otherwise, all rational, non-integer answers need to be expressed as reduced common fractions
except in case of problems dealing with money. In the case of problems requiring dollar answers, answer as a
decimal rounded to the nearest hundredth (ie, to the nearest cent).
All radicals must be simplified and all denominators must be rationalized.
Units are not necessary as part of your answer unless it is a problem that deals with time and in that
case, a.m. or p.m. is required. However, if you choose to use units, they must be correct.
Leave all answers in terms of π where applicable.
Do not round any answers unless stated otherwise.
Record all answers on the colored cover sheets in the answer column only.
Make sure all answer sheets have all the information (name, team number, etc.) at the top of the sheet
filled out.
Tests will be scored as a 0 if answers are not recorded on the answer sheets.
Blank answer sheets and answer sheets with no name will be scored as a 0.
Mental Math – 30 sec per question
8 problems read orally to everyone - Approximately 8% of Individual Score - 25% of team score
When it is time to begin, the proctor will read the first question twice. You may not do any writing or
talking while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You
may not change or cross out answers once you have written an answer down. If there are eraser
marks, write-overs, or crossed-out answers, they will be marked wrong. Once all students have laid
their pencils on the desk, another question will be asked. If a student doesn’t lay his/her pencil down, the
maximum wait time is 30 seconds after completion of the second reading of the question before another
question is asked. You may continue to work on a problem while the next question is being read. The value
of each question is a one or zero. Each student will be asked the same eight questions. Individual scores
used to determine individual placing will be determined by the sum of the Mental Math score and the
Individual Test score for each individual. In addition, the top three Mental Math scores from one team will
be totaled and doubled and will contribute to 25% of the team score.
“Math is Cool” Masters – 2012-13
Sponsored by:
7th & 8th Grade – November 2, 2012
Mental Math Contest
Mental Math – 30 sec per question
8 problems read orally to everyone - Approximately 8% of Individual Score - 25% of team score
When it is time to begin, the proctor will read the first question twice. You may not do any writing or
talking while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You
may not change or cross out answers once you have written an answer down. If there are eraser
marks, write-overs, or crossed-out answers, they will be marked wrong. Once all students have laid
their pencils on the desk, another question will be asked. If a student doesn’t lay his/her pencil down, the
maximum wait time is 30 seconds after completion of the second reading of the question before another
question is asked. You may continue to work on a problem while the next question is being read. The value
of each question is a one or zero. Each student will be asked the same eight questions. Individual scores
used to determine individual placing will be determined by the sum of the Mental Math score and the
Individual Test score for each individual. In addition, the top three Mental Math scores from one team will
be totaled and doubled and will contribute to 25% of the team score.
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Problem
A hiker can hike 5 miles per day. How many miles can the hiker hike in 4
days?
A baby’s head is one-fourth of its total body length. If a baby’s total body
length is 16 inches, what length will its head be, in inches?
The sum of two numbers is 18, while the product of the two numbers is 72.
What is the smaller of the two numbers?
What is the degree measure of each interior angle of a regular nine-sided
polygon?
Express the decimal as a reduced fraction: zero-point-one-two-five
How many distinct positive integer factors does 24 have?
A circle has a diameter of 12 inches. If a square has a side length that is
equal to the radius of this circle, what is the area, in square inches, of the
square?
How many times greater is the area of a circle if the circumference of the
circle triples?
“Math is Cool” Masters – 2012-13
Sponsored by:
November 2, 2012
7th & 8th Individual Contest
Tear this sheet off and fill out top of answer sheet
on following page prior to the start of the test.
GENERAL INSTRUCTIONS applying to all tests:
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Good sportsmanship is expected throughout the competition by all involved, both competitors and
observers. Display of poor sportsmanship may result in disqualification.
Calculators or any other aids may not be used on any portion of this contest.
Unless stated otherwise, all rational, non-integer answers need to be expressed as reduced common fractions
except in case of problems dealing with money. In the case of problems requiring dollar answers, answer as a
decimal rounded to the nearest hundredth (ie, to the nearest cent).
All radicals must be simplified and all denominators must be rationalized.
Units are not necessary as part of your answer unless it is a problem that deals with time and in that
case, a.m. or p.m. is required. However, if you choose to use units, they must be correct.
Leave all answers in terms of π where applicable.
Do not round any answers unless stated otherwise.
Record all answers on the colored cover sheets in the answer column only.
Make sure all answer sheets have all the information (name, team number, etc.) at the top of the sheet
filled out.
Tests will be scored as a 0 if answers are not recorded on the answer sheets.
Blank answer sheets and answer sheets with no name will be scored as a 0.
INDIVIDUAL TEST - 35 minutes
You may NOT be seated next to anyone from your school. If you are MOVE NOW to
avoid being disqualified! When you are prompted to begin, tear off the colored sheet
and begin testing. Make sure your name and school are recorded on the answer sheet.
The raw score will be 2 points for correct answers to problems 1-30 and 3 points for
31-40. Record your answers on the score sheet. No talking during the test. You will be
given a 5 minute time warning.
“Math is Cool” Masters – 2012-13
Sponsored by:
November 2, 2012
7th & 8th Individual Contest
Questions 1-30: 2 points each
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Evaluate:
What is the largest non-positive number?
Write 3,500,000 in scientific notation.
What is the missing number in this geometric sequence? 1, 6, 36, ____, 1296
What is the slope of the line y = 17x+15?
Which fraction is larger?
A = sixty-three over one-hundred twenty-four
B = twenty-four over fifty
Solve for x in this equation:
Only 1/7 of one percent of the mathletes here today will earn a Ph.D. degree in
mathematics. If there are 700 mathletes here today, how many will get a Ph.D. in
mathematics?
Kim is preparing for a party and needs to set up tables for her guests. Each table
is a rectangle and seats 6 guests, 1 on each short end and 2 on each long side. Two
tables with their short ends joined together can only seat 10 guests. Kim is going
to have one long row of tables, made by joining tables at their short ends. How
many tables in all will Kim need to seat herself and 41 guests?
Last year I ate 1500 jelly beans. This year I ate 1750 jelly beans. What was the
percent increase in the number of jelly beans I ate? Answer as a mixed number
percent
Is the product of the first n prime numbers (where n>2) always odd, always even,
or possibly either?
Three angles of a triangle are 3x + 5 degrees, 4x + 6 degrees and 7x + 1 degrees.
What is the value of x?
Austin averaged 73 points on the 4 drive tests that he took before getting his
license. He got a 65, 70, and 75 on the test the first three times, failing the test.
What was his 4th (passing) score?
14
Find the area of this rectangle, in square centimeters.
12 cm
30°
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16
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18
19
20
21
22
23
Jay invests $3000 at a fixed annual rate of 3%, compounded annually. After 2
years, how much money will he have? Answer in dollars, to the nearest cent.
What is the least common multiple of the greatest common factor of 60 and 105
and the greatest common factor of 72 and 153?
How many ways are there to seat 3 students in 4 desks?
Lisa has three stacks of stickers. The second stack has
first and the third stack has
more stickers than the
more stickers than the second. How many stickers
does the first stack have if there are 555 stickers total?
Joe has two coupons he could use in buying a desk that originally sells for $400.
One coupon is for $50 off and the other coupon is for 15% off. Using one of these
coupons, what is the largest number of dollars Joe could save, compared to the
original price?
Using quarters, dimes and nickels, how many ways are there to make change for
one dollar?
What is the slope of the line that goes through the points (1,3) and (-2, 4)
Write a 3 digit number using 3 distinct digits. Reverse the digits. What is the
maximum positive difference between the two numbers? Zero cannot be used as
an end number.
What relationship proves that ABD is congruent to ACD?
A.
B.
C.
D.
E.
AAS
SAS
AAA
ASA
SSS
A
B
C
D
24
160 acres is an area of land equal to the area of a square that is ½ mile on each
side. This summer one of the many fires in the state of Washington grew to
38,400 acres. In square miles, how large was this one fire?
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30
Given that Ax+B=C, solve for x in terms of A, B, and C.
The sum of 4 consecutive even numbers is 4x + 12 where x is the first number.
Write an expression for the last number.
Tell whether the reasoning process is deductive or inductive:
Ramon noticed that spaghetti had been on the school menu for the past five
Wednesdays. Ramon decides that the school always serves spaghetti on
Wednesday.
What is the shortest possible integer length of the other side of a triangle with
side lengths 135 and 73 units?
How many different paths are there from the upper left corner
to the lower right corner of the figure if movement can only be
down or to the right?
Which net makes the following shape? Answer A, B, C, or D.
A)
B
C) Neither A or B
D) Both A and B
Challenge Questions: 3 pts each
31
OABC is a parallelogram. Give the location of point B as an ordered pair (x, y).
C (3, 5)
O
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35
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38
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40
B (x, y)
A (8, 0)
A square piece of paper is folded in half twice, first from top to bottom and then again
from top to bottom. The final piece of folded paper has a perimeter of 50 units. What is
the perimeter of the original piece of paper?
Assume a ream of 500 sheets of paper is 5 cm thick. If one sheet of paper could be
removed and folded in half 20 times, how many meters thick (to the nearest meter) would
the folded paper be?
Billy has built a straight fence 60 feet long, with a post at each end and one every 10 feet.
He starts at a randomly selected post and paints it completely. He then selects another
unpainted post (not necessarily a post 10 feet away) and completely paints it, then selects
another unpainted post, and so forth. When all posts are painted, he stops. What is the
maximum distance in feet that Billy could travel while painting the posts?
Buttercup, Fruitloop and Stinkeye are scheduled to run a race with probabilities of winning
the race of 1/7, 2/13 and 64/91, respectively. Stinkeye went color-blind and was unable to
race. What is the probability that Buttercup will win?
It takes 5 workers 3 days to do 8 jobs. Assuming all workers work at the same rate and
all jobs are equal, how many workers will it take to do 12 jobs in 4 days?
Order the numbers from lowest to highest using the four letters:
A. -4.6 x 10-9
B. -3 x 103
C. -9.6 x 10-7
D. 2 x 104
The number of reps Alex can do lifting watermelons is inversely proportional to the square
of the weight of the watermelons. If he can lift a four-pound baby 36 times, how many
times can he lift a twelve-pound watermelon?
There is a point (3, 2). Reflect that point across a line with the equation y = x + 1. What
are the new coordinates of the reflected point?
In a room are 6 people whose birthdays are randomly distributed. What is the percent
probability that at least two of the people share a birthday? Give your answer rounded to
the nearest whole percent.
“Math is Cool” Masters – 2012-13
Sponsored by:
8th Grade – November 2, 2012
Individual Multiple Choice Contest
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Farmer Frank took a load of carrots to market and sold all of them. The carrots were
grouped by size (small, medium, and large). Below is a partial table of data. Use the
following information to answer questions 1 – 5.
Size
Number of Total weight ??
Selling price Total earned
carrots
in pounds
per pound
Small
830
415
8 ounces
10¢
$41.50
Medium ??
1350
1 pound 2
12¢
??
ounces
Large
900
1350
1 pound 8
??
$189.00
ounces
What was total amount Farmer Frank earned?
A) $41.50
B) $162.00 C) $189.00
D) $392.50
E) Answer not given.
What was the price per pound that Farmer Frank was paid for his large carrots?
A) 10¢
B) 12¢
C) 14¢
D) 16¢
E) Answer not given.
What is the best title for the fourth column?
A) Weight of the container B) Average (mean) weight per carrot
C) Maximum weight
per carrot
D) Weight of 100 carrots
E) Minimum weight per carrot
What is the average price paid per pound for all the carrots, rounded to the nearest whole
penny?
A) 10¢
B) 12¢
C) 14¢
D) 16¢
E) Answer not given.
How many medium carrots did Farmer Frank take to market?
A) 830
B) 900
C) 1000
D) 1200
E) Answer not given.
John-Jacob Jingle-Heimer-Schmitt and his wife Jenny-Jacob Jingle-Heimer- Schmitt are
deciding how much of their income they can allocate to buying a new car. They allocate 1/8
of their income to food, 1/6 of their income to utilities, 1/12 of their income to baby
supplies, and 1/3 of their income to savings, and have no other expenses. What fraction of
their income can they allocate to buying a car?
A) 1/4
B) 1/6
C) 7/24
D) 3/7
E) Answer not given
John-Jacob Jingle-Heimer-Schmitt Junior drinks 1 quart of milk every 12 hours. If milk is
$4.50 a gallon, how much money will John-Jacob Jingle-Heimer-Schmitt have to spend on
milk in a non-leap year?
A) $821.25
B) $1,642.50 C) $3,285.00 D) $1,094.99
E) Answer not given.
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10
If it takes Jeremy 18 hours to dig a cubical hole 2 meters on an edge, how many hours
would it take him (digging at the same rate) to dig a cubical hole 4 meters on an edge?
A) 36 hours B) 72 hours C) 144 hours D) 288 hours
E) Answer not given.
This contest (with 10 problems) is scored 2 for a correct answer, 0 if the answer is left
blank, and -1 if the answer is incorrect. A student has N correct answers and receives a
score of 5. The number of possible values of N is
A) 0
B) 3
C) 4
D) 5
E) Answer not given.
For a clock with an hour hand and a minute hand, how fast is the hour hand moving, in
degrees per minute?
A) 6
B) 5
C) 12
D) 0.5
E) Answer not given.
“Math is Cool” Masters – 2012-13
Sponsored by:
8th Grade – November 2, 2012
Team Contest
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Let A = π , B = 9 , C =
10
( )
2
, and D = 1.7 . Put these four values in order of increasing size (smallest
3
first). Your answer should be 4 letters in the correct order.
Find the value of x if 4x − 29 = x − 8 .
A cherry pudding recipe makes six servings of a dessert with 2012 total calories. One serving of this
cherry pudding will be what percent of a 2000-calorie daily diet? Round your answer to the nearest
whole percent.
What is the sum of all counting numbers that will divide into 2012 without remainder?
2
2
2⎞
2
2
⎛
⎛
Find the value of: ⎜⎜ 3 + 1 + 5 − 3 ⎟⎟ − 6 + 2 − ⎜⎜ 3 + 3 + 0 − 1
⎠
⎝
⎝
( ) (
)
⎞
( ) ( ) ( ) ⎟⎟⎠
2
A square pyramid whose height and base side lengths are all the same has a volume of 72 cubic inches.
What is the area of the base, in square inches?
What is the sum of all 2-digit positive multiples of 4, for which the sum of its digits and the product
of its digits are both positive multiples of 4?
Ann, Ben, Con, Dan, and Evan are standing in line. In how many orders could they be standing if Ann
and Ben are next to each other, but Con and Dan are not next to each other?
The sum of 15 and its digits is 21, since 15 + 1 + 5 = 21. Find a 4-digit counting number such that the
sum of the number and its digits is 4377.
Let R =
P +Q
2
and P < Q < 50 . For how many values of R could P , Q , and R all be prime numbers?
“Math is Cool” Masters – 2012-13
Sponsored by:
8th Grade – November 2, 2012
Pressure Round Contest
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2
3
What is the volume in cubic units of a cone with a slant height of 13 units and a
radius of 5 units?
How many times do you have to flip a fair coin to have less than a 10% chance of
getting all heads?
4
Hugh is building a sidewalk, in the shape of a rectangular prism, that is 4 feet
wide, 5 inches thick, and 10 yards long. How many cubic yards of concrete are
needed to make the sidewalk? Write the answer as a mixed number.
Two squares each with side 14 cm are placed so that a vertex of one lies at the
center of the other. Find the area of the shaded region, in square centimeters.
5
Two similar polygons are shown. Find the sum of the values of x, y, and z. If your
answer is not a whole number, give it as a reduced fraction.
20
x
18
y
16
12
26
z
“Math is Cool” Masters – 2012-13
Sponsored by:
8th Grade – November 2, 2012
COLLEGE KNOWLEDGE BOWL ROUND #1 –
SET 1
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Problem
Answer
1
2
3
4
In how many orders can six different books be arranged in a row?
720 [ways]
What is the sum, in degrees, of the interior angles of a heptagon?
900 [degrees]
What is the least common multiple of 36 and 99?
396
A bag of M&M’s contains 12 red, 18 blue, and 6 green M&M’s. If you
pick three M&M’s at random and without replacement, what is the
probability that you will pick a blue, a green, and a red in that order?
Answer as a reduced fraction.
The number of diagonals that can be drawn in a certain polygon is 14.
What is the sum, in degrees, of the exterior angles of this polygon?
18/595
What is the surface area in square units of a sphere with diameter 8
units?
64 pi [sq. units]
James has been trying to get his driver’s license for six years. He
takes the test every month, plus one extra time in February each
year. He has to pay $20 to take the test each time. How much has
he spent so far on driver’s license tests?
A cup of coffee at 175 degrees Fahrenheit cools at 3 point 5
degrees Fahrenheit per 6 minutes. How many minutes will it take to
cool to 140 degrees Fahrenheit?
All the clowns in a certain circus act are identical in size and shape.
Each clown is 6 feet tall, while two clowns together are 11 feet 6
inches tall when one stands on the other’s shoulders. How many feet
tall are three clowns together when a third stands on the second
clown’s shoulders?
Brian is traveling at 15,840 feet per hour. What is Brian’s rate of
speed in miles per hour?
1560 [dollars]
5
6
7
8
9
10
360 [degrees]
60 [minutes]
17 [feet]
3 [miles per hour]
“Math is Cool” Masters – 2012-13
Sponsored by:
8th Grade – November 2, 2012
COLLEGE KNOWLEDGE BOWL ROUND #2 –
SET 2
#
Problem
Answer
1
2
3
Walt walked 2680 miles across the US. If each of his steps is one
and a half feet long, how many steps did Walt take to cross the US?
9,433,600 [steps]
What is the area in square units of a rhombus with diagonals of 10
and 8 units?
40
Yesterday Emily worked 10 hours at six dollars per hour. How many
hours would it take her to earn the same amount of money if she was
earning twelve dollars per hour?
Richard and Stacey started dating on July 28th and have a date
every day. On what date (month and day) will they have their 100th
date?
What is the probability that the roll of two fair six-sided dice yields
a sum of five or greater?
5 [hours]
Stacey loves the feeling of new socks, so she buys a new $12 pair
every day for the first three months of 2012. How many dollars did
Stacey spend for these socks?
What is the sum of the 5th positive triangular number, the 5th
positive square number and the 5th positive even number?
1092 [dollars]
What is the overall average weight in pounds of 8 fish if 3 of the
fish average 4 pounds apiece and the other 5 fish average 12 pounds
apiece?
A box and the chocolates in it together weighed two point two
pounds. After I removed three-fourths of the chocolate (by
weight), the box and the remaining chocolates weighed point seven
pounds. What is the weight of the box, in pounds? Give your answer
as a decimal.
The price one gallon of gas was 3 dollars and fifty cents. The price
went up by 20%, and then down by 10%. What is the new price in
dollars of a gallon of gas?
9 [pounds]
4
5
6
7
8
9
10
November 4th
11-4
5/6
50
0.2 [pounds]
[point 2, zero
point 2, or twotenths]
[$] 3.78
or
“Math is Cool” Masters – 2012-13
Sponsored by:
8th Grade – November 2, 2012
COLLEGE KNOWLEDGE BOWL ROUND #3 –
SET 3
#
Problem
Answer
1
I start with 3 Twitter followers. If I gain 4 Twitter followers the
first day and every day thereafter and don’t lose any followers, how
many followers will I have after 3 consecutive, non-leap years?
What is the area, in square units, of a triangle with side lengths 12
units, 16 units and 20 units?
4383 [followers]
What is the volume, in cubic centimeters, of a right circular cone
with a radius of 6 centimeters and a height of 9 centimeters?
108 pi [cubic
centimeters]
George drives his car 4 miles at 8 miles per hour, and then drives
another 4 miles at 10 miles per hour. What is his average speed, in
miles per hour? Give your answer as a reduced fraction.
Stacey started writing College Bowl questions at 8:00 PM and
stopped at 10:40 PM. What is the number of degrees travelled
during this time by the minute hand of a clock?
How many counting numbers between 100 and 200 are divisible by
11?
80/9
Jerry takes two hours to paint a fence by himself. Hiko takes six
hours to paint the same fence by himself. How many minutes does it
take them to paint a fence together?
A block of wood in the shape of a rectangular prism measured 10
inches by 6 inches by 1 foot. Lance cut this block into smaller
rectangular prisms measuring 2 inches by 2 inches by 2 inches.
What is the maximum number of smaller prisms he could get?
The ratio of boys to girls on a math team is 3 to 8. If the math
team has 99 members, how many members are girls?
90 [minutes]
A train measuring 1 mile in length travels through a tunnel 4 miles
long. If the train travels at 30 miles per hour, how many minutes will
the entire train be inside the tunnel?
6 [minutes]
2
3
4
5
6
7
8
9
10
96 [square units]
960 [degrees]
9 [numbers]
90 [prisms]
72 [members]
“Math is Cool” Masters – 2012-13
Sponsored by:
8th Grade – November 2, 2012
COLLEGE KNOWLEDGE BOWL ROUND #4 –
SET 4
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Problem
Answer
1
2
3
4
5
6
7
8
What is 2 to the power of 3, plus 2 to the power of 4, plus 3 to the
power of 3?
51
A right triangle has a hypotenuse of 26 units and a leg of 10 units.
How many units long is the other leg?
24 [units]
When x equals 3, what is the value of x squared, plus 17 times x, plus
35?
95
Solve for x in the following equation: 15x plus 3 equals 63
[x=] 4
What is the distance between the points THREE COMMA NINE and
NEGATIVE SEVEN COMMA NINE?
10 [units]
Billy made 25 out of 30 shots in basketball. What is the longest
streak of consecutive shots that he must have made?
5 [shots]
How many positive integer factors does 36 and 48 have in common?
6 [divisors]
The area of a rectangle is 255 square feet. The width of the
rectangle is 17 feet. What is the number of feet in the perimeter
of the rectangle?
What is the smallest of three consecutive counting numbers such
that their product is 9240?
64 [feet]
A rectangle with width 4 centimeters and length 10 centimeters has
the same perimeter as a certain square. How much larger, in square
centimeters, is the area of the square than the area of the
rectangle?
9 [square
centimeters]
9
10
20
“Math is Cool” Masters – 2012-13
Sponsored by:
8th Grade – November 2, 2012
COLLEGE KNOWLEDGE BOWL ROUND #5 –
SET 5
#
Problem
Answer
1
2
How many prime numbers are there between 50 and 60?
2 [primes]
I like pie. Every Monday, I eat 6 pies. For the next 4 days each
week, I eat 4 pies a day. On weekends, I eat a total of 20 pies. On
average, how many pies do I eat a day?
What is the volume, in cubic units, of a cylindrical soup can with a
radius of 2 units and a height of 3 units?
6 [pies]
A winch has a spool with a radius of 3 units. It turns at one
revolution every 10 seconds. How many minutes does it take to reel
in a rope that is 108 pi units in length?
The first two terms of the Fibonacci sequence are both 1, and each
later term is formed by adding the two previous terms. What is the
twelfth term of the Fibonacci sequence?
What is the midpoint of the line segment that connects the point
TWO COMMA FIVE and the point SIX COMMA FIFTEEN? Give your
answer as an ordered pair (x,y).
Miya is an avid runner. She starts a 10-day workout routine. On the
first day, she runs 10 miles. On each subsequent day, she runs 4
more miles than the previous day. How many total miles will Miya
have run by the end of the 10-day workout?
What is the least possible total number of days in any three
consecutive months?
3 [minutes]
A ream of paper containing 500 sheets is 8 centimeters thick. How
many sheets of paper are in a stack five and six-tenths centimeters
high?
Find the perimeter, in inches, of an isosceles trapezoid with base
lengths of 4 and 10 inches, and height 4 inches.
350 [sheets]
3
4
5
6
7
8
9
10
12 pi [cubic units]
144
(4,10) or four
comma ten
280 [miles]
90 [days]
24 [inches]
“Math is Cool” Masters – 2012-13
Sponsored by:
8th Grade – November 2, 2012
COLLEGE KNOWLEDGE BOWL ROUND #6 –
#
1
2
3
4
5
6
7
8
9
10
SET 6
Problem
Answer
A right triangle has legs of 27 inches and 36 inches. How many
inches long is its hypotenuse?
45 [inches]
Solve for X if two raised to the power 3X is equal to 8.
[x=] 1
Martha rolls two cubical dice. As a reduced fraction, what is the
probability that the sum of the two numbers she rolls is 8?
5/36
What is the units digit of the result when seven is raised to the
thirtieth power?
9
What is the cube root of sixty-four?
4
What is the height in inches of a right circular cone with a base area
of 81 pi and a volume of 108 pi?
4 [inches]
The sum of two numbers is 36, and their difference is 8. What is
their product?
308
Forty-two minutes after 11 AM is how many minutes before 2 PM?
138 [minutes]
The product of two prime numbers is 247. What is the positive
difference between these two prime numbers?
6
Joan selects twenty consecutive three-digit counting numbers. She
divides each of them by 20 and records each remainder. What is
the sum of the twenty remainders?
190
“Math is Cool” Masters – 2012-13
th
Sponsored by:
7 & 8th Grade – November 2, 2012
COLLEGE KNOWLEDGE BOWL ROUND –
EXTRA
#
Problem
Answer
1
2
The total value of 500 nickels equals the total value of how many
quarters?
100 [quarters]
On a certain train trip, Hank travels at a constant speed. By 11 AM,
he had completed one-fourth of the trip. By 2 PM, he had completed
five-eighths of the trip. How many hours did it take him to complete
the entire trip?
What number does N stand for, if 6 to the power of N is 216?
8 [hours]
3
3
Final Score:
KEY
“Math is Cool” Masters -- 2012-13
School:_______________________ Room #
Name:
Team #____
(Out of 8)
Proctor: _________________
7th & 8th Grade
Mental Math – 30 sec per question
8 problems read orally to everyone - Approximately 8% of Individual Score - 25% of team score
When it is time to begin, the proctor will read the first question twice. You may not do any writing or talking
while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You may not
change or cross out answers once you have written an answer down. If there are eraser marks, writeovers, or crossed-out answers, they will be marked wrong. Once all students have laid their pencils on
the desk, another question will be asked. If a student doesn’t lay his/her pencil down, the maximum wait
time is 30 seconds after completion of the second reading of the question before another question is asked.
You may continue to work on a problem while the next question is being read. The value of each question is a
one or zero. Each student will be asked the same eight questions. Individual scores used to determine
individual placing will be determined by the sum of the Mental Math score and the Individual Test score for
each individual. In addition, the top three Mental Math scores from one team will be totaled and doubled
and will contribute to 25% of the team score.
Answer
1
2
3
4
5
6
7
8
20 [miles]
4 [in]
6
140 [degrees]
1/8
8 [factors]
36 [in2]
9 [times greater]
1 or 0
1 or 0
Final Score:
Math is Cool” Masters – 2012-13
8th Grade – November 2, 2012
Student Name__________________________________
Proctor Name__________________________________Room #_______
SCHOOL NAME______________________ Team #
KEY
First Score
(out of 20)
INDIVIDUAL MULTIPLE CHOICE - 15 minutes – 10 problems – 20% of team score
This test is the only test where you will be penalized for incorrect responses. You will receive 2 points
for a correct letter response, 0 points for leaving it blank and -1 point for an incorrect response. It is
not necessary to write your personal name on the test, but you may put it at the bottom of the test so
your coach will be able to give you back the correct test. This test is taken individually, but it is part of
your team score, including zeros for missing team members. Your team score will be calculated by taking
the mean of your four team members’ scores. When you are prompted to begin, tear off the colored
sheet and begin testing. Since this is a multiple choice test, ONLY a letter response should be
indicated as an answer on the answer sheet. No talking during the test.
DO NOT WRITE IN SHADED REGIONS
Answer
1
2
3
4
5
6
7
8
9
10
10
D
C
B
E [13¢]
D
C
A
C
B
D
-1, 0 or 2
-1, 0 or 2
“Math is Cool” Masters – 2012-13
8th Grade – November 2, 2012
SCHOOL NAME__________________________Team #
Proctor Name__________________________________Room #_______
Final Score:
KEY
First Score
(out of 10)
Team Contest – Score Sheet
TEAM TEST - 15 minutes – 30% of team score
When you are prompted to begin, tear off the colored sheet and give a copy of the test to each of your
team members and begin testing. Each problem is scored as 1 or 0. Record all answers on the colored
answer sheet.
DO NOT WRITE IN SHADED REGIONS
1
2
3
4
5
6
7
8
9
10
10
Answer
DBAC
[x=] 7
17 [%]
3528
299
36 [sq inches]
264
24 [orders]
4362
10 [values]
1 or 0
1 or 0
“Math is Cool” Masters – 2012-13
8th Grade – November 2, 2012
Proctor Name__________________________________Room #_______
Final Score:
KEY
First Score
SCHOOL NAME___________________________________Team #
PRESSURE ROUND - 10 minutes – 5 problems - 5 rounds – 15% of team score
When it is time to begin, you will be handed a packet of five problems. There is a copy of the problems
for each team member. Two minutes after the start of the test you are expected to submit an answer
for one of the problems (it can simply be a guess). The maximum value of this answer is 1 point. In
another two minutes you are expected to submit another answer to one of the four remaining problems;
its maximum value is two points. This process will continue until all the problems are answered and each
consecutive problem’s worth will go up by one point. You must submit your answers on the colored sheets
given to you. If you do not have an answer at the end of a two minute period, you must still submit an
answer sheet with an identified problem number on it. Failure to do so will result in loss of points. This
event is timed, and you will be given a verbal 5 second warning and told to hold your answer sheet up in
the air. You may keep working as the sheets are collected. If a team answers the same question more
than once, only the first answer will be scored and the other attempts will be ignored.
Pressure Round Answers
Answer
1
2
3
4
5
10
[cubic units]
4 [times]
1
23
27
[cubic yards]
49 [sq cm]
117/2
Final Score:
“Math is Cool” Masters -- 2012-13
School:_______________________ Room #
Name:
Team #____
(Out of 8)
Proctor: _________________
8th Grade
Mental Math – 30 sec per question
8 problems read orally to everyone - Approximately 8% of Individual Score - 25% of team score
When it is time to begin, the proctor will read the first question twice. You may not do any writing or talking
while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You may not
change or cross out answers once you have written an answer down. If there are eraser marks, writeovers, or crossed-out answers, they will be marked wrong. Once all students have laid their pencils on
the desk, another question will be asked. If a student doesn’t lay his/her pencil down, the maximum wait
time is 30 seconds after completion of the second reading of the question before another question is asked.
You may continue to work on a problem while the next question is being read. The value of each question is a
one or zero. Each student will be asked the same eight questions. Individual scores used to determine
individual placing will be determined by the sum of the Mental Math score and the Individual Test score for
each individual. In addition, the top three Mental Math scores from one team will be totaled and doubled
and will contribute to 25% of the team score.
Answer
1
2
3
4
5
6
7
8
20 [miles]
6
140 [degrees]
300 [Pounds]
1/8
8 [factors]
[$]27 or [$]27.00
9 [times greater]
1 or 0
1 or 0
Final Score:
Math is Cool” Masters – 2012-13
8th Grade – November 2, 2012
Student Name__________________________________
Proctor Name__________________________________Room #_______
SCHOOL NAME______________________ Team #
First Score
(out of 20)
INDIVIDUAL MULTIPLE CHOICE - 15 minutes – 10 problems – 20% of team score
This test is the only test where you will be penalized for incorrect responses. You will receive 2 points
for a correct letter response, 0 points for leaving it blank and -1 point for an incorrect response. It is
not necessary to write your personal name on the test, but you may put it at the bottom of the test so
your coach will be able to give you back the correct test. This test is taken individually, but it is part of
your team score, including zeros for missing team members. Your team score will be calculated by taking
the mean of your four team members’ scores. When you are prompted to begin, tear off the colored
sheet and begin testing. Since this is a multiple choice test, ONLY a letter response should be
indicated as an answer on the answer sheet. No talking during the test.
DO NOT WRITE IN SHADED REGIONS
Answer
1
2
3
4
5
6
7
8
9
10
10
D
C
B
E [13¢]
D
C
A
C
B
D
-1, 0 or 2
-1, 0 or 2
“Math is Cool” Masters – 2012-13
Final Score:
8th Grade – November 2, 2012
SCHOOL NAME__________________________Team #
Proctor Name__________________________________Room #_______
First Score
(out of 10)
Team Contest – Score Sheet
TEAM TEST - 15 minutes – 30% of team score
When you are prompted to begin, tear off the colored sheet and give a copy of the test to each of your
team members and begin testing. Each problem is scored as 1 or 0. Record all answers on the colored
answer sheet.
DO NOT WRITE IN SHADED REGIONS
1
2
3
4
5
6
7
8
9
10
10
Answer
DBAC
[x=] 7
17 [%]
3528
299
36 [sq inches]
264
24 [orders]
4362
10 [values]
1 or 0
1 or 0
Final Score:
“Math is Cool” Championships – 2012-13
KEY
November 2, 2013
STUDENT NAME:
Proctor Name:
School Name:
Team #:
th
th
7 & 8 Grade Individual Contest – Score Sheet
DO NOT WRITE IN SHADED REGIONS
1
2
3
4
5
6
7
8
9
10
Answer
3
0
3.5 x 106
216
17
A [or 63/124]
[x=] 17/9
1 [mathlete]
10 [tables]
[%]
1 or 0
1 or 0
16
17
18
19
20
21
22
23
24
25
Answer
45
24 [ways]
148 [stickers]
[$] 60 or [$] 60.00
29 [ways]
-1/3
792
A
60 [square miles]
[x=]
11
even
26
x+6
12
13
[x=] 12
27
28
inductive
29
30
252 [paths]
14
15
82 [points]
[sq cm]
[$] 3182.70
1-15 TOTAL:
63 [units]
B
16-30 TOTAL:
1 or 0
1 or 0
31
32
33
34
35
36
37
38
39
40
Room #:
Answer
(11, 5)
80 [units]
105 [meters]
230 [feet]
13/27
6 [workers]
BCAD
4 [times]
(1,4)
4 [%]
31-40 TOTAL:
7th & 8th Grade
1 or 0
1 or 0